Department of Mathematics
Alfred P. Sloan Fellow
My research interests are in the area of applied mathematics with emphasis on mathematical biology. In particular, I work on the design and analysis of mathematical models of biological systems within the framework of theories of continuum mechanics, dynamical systems, and stochastic dynamics.
Inverse problem for ODE modelsThe utility of any mathematical model is crucially dependent on how well such a model represents the reality. Scientists use various mathematical and statistical tools to make the connection between observed data and model behavior. I am interested in reserach on fundamental questions associated with parameter inference. With my students and collaborators we have studied the existence and uniqueness of parameters for which models reproduces observed data, inferred parameter distributions for ensemble models of in-host immune response, and computed the maximal uncertainty in the data that can be tolerated for a model to predict a robust type of behavior. Our current research is focused on quantifying the uncertainty of model predictions.
Mathematical ImmunologyI am interested in the development of mathematical models of in-host human immune response to viral and bacterial infections, and in the relation between immunity and inflammation. With my collaborators we have developed an ODE model for individual response to influenza virus infections and an ensemble model capable of characterizing probabilistic outcomes of treatment scenarios. We have also developed a model of bacterial pneumonia and analyzed the dependence of the observed behavior on the characteristics of the host and bacterial strains.
DNA mechanicsMy current projects include the development micromechanical models of DNA elasticity that combine atomic-scale and continuum mechanics approaches with recent advances in computational chemistry and employ information obtained by X-ray crystallography, single-molecule manipulation, and other experimental techniques. Part of my research program is oriented towards continuum modeling of complex macromolecular assemblies and the application of stochastic and deterministic dynamics in the study of molecular biological processes.
Cell MigrationWe are developing a mathematical model of migration of enterocytes during intestinal wound healing process that is based on novel assumption of elastic deformation of the cell layer and incorporates cell mobility, adhesion and proliferation.
Math KangarooWith my colleague Piotr Hajlasz I organize a local testing site for Math Kangaroo, international mathematical competition for children grades 2-12. For more information see the link on the left or our article in Post-Gazette.